Photonic bandgap optical waveguidewith anti-resonant core boundary

ABSTRACT

Improved photonic band-gap optical fibre. The present invention relates in particular to improved photonic band-gap optical fibres that can confine light to a core region of the fibre by the action of both a photonic band-gap cladding and an antiresonant core boundary, at the interface between the core and cladding. According to embodiments of the present invention, a fibre has a core, comprising an elongate region of relatively low refractive index, a photonic bandgap structure arranged to provide a photonic bandgap over a range of wavelengths of light including an operating wavelength of light, the structure, in a transverse cross section of the waveguide, surrounding the core and comprising elongate relatively low refractive index regions interspersed with elongate relatively high refractive index regions and a relatively high refractive index boundary at the interface between the core defect and the photonic bandgap structure, the boundary having a thickness around the core such that the boundary is substantially anti-resonant at the operating wavelength of the fibre. In preferred embodiments, the core boundary is a relatively constant thickness region of glass around a hollow core.

The present invention is in the field of optical waveguides and relatesin particular, but not exclusively, to optical waveguides that guidelight by virtue of a photonic bandgap.

Optical fibre waveguides, which are able to guide light by virtue of aso-called photonic bandgap (PBG), were first proposed in 1995.

In, for example, “Full 2-D photonic bandgaps in silica/air structures”,Birks et al., Electronics Letters, 26 Oct. 1995, Vol. 31, No. 22,pp.1941-1942, it was proposed that a PBG may be created in an opticalfibre by providing a dielectric cladding structure, which has arefractive index that varies periodically between high and low indexregions, and a core defect in the cladding structure in the form of ahollow core. In the proposed cladding structure, periodicity wasprovided by an array of air holes that extended through a silica glassmatrix material to provide a PBG structure through which certainwavelengths of light could not pass. It was proposed that light coupledinto the hollow core defect would be unable to escape into the claddingdue to the PBG and, thus, the light would remain localised in the coredefect.

It was appreciated that light travelling through a hollow core defect,for example filled with air or even under vacuum, would suffersignificantly less from undesirable effects, such as non-linearity andloss, compared with light travelling through a solid silica or dopedsilica fibre core. As such, it was appreciated that a PBG fibre may findapplication as a transmission fibre to transmit light between atransmitter and a receiver over extremely long distances, for exampleunder the Atlantic Ocean, without undergoing signal regeneration, or asa high optical power delivery waveguide. In contrast, for standardindex-guiding, single mode optical fibre, signal regeneration istypically required approximately every 80 kilometres.

The first PBG fibres that were attempted by the inventors had a periodiccladding structure formed by a triangular lattice of circular air holesembedded in a solid silica matrix and surrounding a central air coredefect. Such fibres were formed by stacking circular or hexagonalcapillary tubes, incorporating a core defect into the cladding byomitting a single, central capillary of the stack, and then heating anddrawing the stack, in a one or two step process, to form a fibre havingthe required structure.

International patent application PCT/DK99/00193 describes various PBGfibre structures, for example having a cladding region based on ahoneycomb lattice with a central air core. The air core is the same sizeas holes in the cladding region. The structure of the cladding producesa PBG and the air core, which creates a defect in the cladding, enableslight to be guided in the glass in the locality of the air core.

International patent application PCT/GB00/01249 (The Secretary of Statefor Defence, UK), filed on 21 Mar. 2000, proposed the first PBG fibre tohave a so-called seven-cell core defect, surrounded by a claddingcomprising a triangular lattice of air holes embedded in an all-silicamatrix. The core defect was formed by omitting an inner capillary and,in addition, the six capillaries surrounding the inner capillary, from apreform used to make the fibre. This fibre structure was seen to guideone or two modes in the core defect, in contrast to the previous,single-cell core defect fibre, which appeared not to support any guidedmodes in the core defect.

According to PCT/GB00/01249, it appeared that the single-cell coredefect fibre, by using analogous calculations to the density-of-statescalculations of solid-state physics, would only support approximately0.23 modes. That is, it was not surprising that the single-cell coredefect fibre appeared to support no guided modes in its core defect. Incontrast, based on the seven-fold increase in core defect area(increasing the core defect radius by a factor of √7), the seven-cellcore defect fibre was predicted to support approximately 1.61 spatialmodes in the core defect. This prediction was consistent with thefinding that the seven-cell core defect fibre did indeed appear tosupport at least one guided mode in its core defect.

A preferred fibre in PCT/GB00/01249 was described as having a coredefect diameter of around 15 μm and an air-filling fraction (AFF)—thatis, the proportion by volume of air in the cladding—of greater than 15%and, preferably, greater than 30%.

In “Analysis of air-guiding photonic bandgap fibres”, Optics Letters,Vol. 25, No. 2, Jan. 15, 2000, Broeng et al. provided a theoreticalanalysis of PBG fibres. For a fibre with a seven-cell core defect and acladding comprising a triangular lattice of near-circular holes,providing an AFF of around 70%, the structure was shown to support oneor two air guided modes in the core defect. This was consistent with thefinding in PCT/GB00/01249.

In the chapter entitled “Photonic Crystal Fibers: Effective Index andBand-Gap Guidance” from the book “Photonic Crystal and LightLocalization in the 21^(st) Century”, C. M. Soukoulis (ed.), ©2001Kluwer Academic Publishers, the authors presented further analysis ofPBG fibres based primarily on a seven-cell core defect fibre. Theoptical fibre was fabricated by stacking and drawing hexagonal silicacapillary tubes. The authors suggested that a core defect must be largeenough to support at least one guided mode but that, as in conventionalfibres, increasing the core defect size would lead to the appearance ofhigher order modes. The authors also went on to suggest that there aremany parameters that can have a considerable influence on theperformance of bandgap fibres: choice of cladding lattice, latticespacing, index filling fraction, choice of materials, size and shape ofcore defect, and structural uniformity (both in-plane and along the axisof propagation).

WO 02/075392 (Corning, Inc.) identifies a general relationship in PBGfibres between the number of so-called surface modes that exist at theboundary between the cladding and core defect of a PBG fibre and theratio of the radial size of the core defect and a pitch of the claddingstructure, where pitch is the centre to centre spacing of nearestneighbour holes in the triangular lattice of the exemplified claddingstructure. It is suggested that when the core defect boundary, togetherwith the photonic bandgap crystal pitch, are such that surface modes areexcited or supported, a large fraction of the “light power” propagatedalong the fibre is essentially not located in the core defect.Accordingly, while surface states exist, the suggestion was that thedistribution of light power is not effective to realise the benefitsassociated with the low refractive index core defect of a PBG crystaloptical waveguide. The mode energy fraction in the core defect of thePBG fibre was shown to vary with increasing ratio of core defect size topitch. In other words, it was suggested that the way to increase modeenergy fraction in the core defect is by decreasing the number ofsurface modes, in turn, by selecting an appropriate ratio of the radialsize of the core defect and a pitch of the cladding structure. Inparticular, WO 02/075392 states that, for a circular core structure, aratio of core radius to pitch of around 1.07 to 1.08 provides a highmode power fraction of not less than 0.9 and the structure is singlemode guiding. Other structures are considered, for example in FIG. 7therein, wherein the core defect covers an area equivalent to 16cladding holes.

The reason why varying the ratio of the radial size of the core defectand a pitch of the cladding structure affects the nature of the surfacemodes supported by a PBG fibre can be explained with reference to thebook “Photonic Crystals: Molding the Flow of Light”, Joannopoulos etal., Princeton University Press, ISBN 0-691-03744. The text describes indetail the nature of surface modes and, in particular, the reasons whythey form at an interface between a PBG structure and a defect (or othertermination of the PBG structure). In brief, surface modes occur whenthere are electromagnetic modes near the surface, but they are notpermitted to extend into the PBG crystal at the respective frequency dueto the PBG. The book goes on to describe that the characteristics, andindeed the presence at all, of the surface modes can be tuned by varyingthe termination position of the PBG structure. For example, a PBGstructure that terminates by cutting through air holes has differentsurface mode characteristics than the same PBG structure that terminatesby cutting through only solid material around holes. WO 02/075392 isconsistent with this since varying the core defect size of a PBG fibrenaturally varies the termination position of the PBG structure.

In a Post-deadline paper presented at ECOC 2002, “Low Loss (13 dB) Aircore defect Photonic Bandgap Fibre”, N. Venkataraman et al. reported aPBG fibre having a seven-cell core defect that exhibited loss as low as13 dB/km at 1500 nm over a fibre length of one hundred metres. Thestructure of this fibre closely resembles the structure considered inthe book chapter referenced above. The authors attribute the relativelysmall loss of the fibre as being due to the high degree of structuraluniformity along the length of the fibre.

More recently, the present applicant has presented a post-deadline paperat OFC 2004: “Low loss (1.7 dB/km) hollow core photonic bandgap fiber”,Mangan et al. This paper reports the lowest loss result ever achieved bya PBG fibre and goes on to propose that scaling the fibre to operate ata longer wavelength should reduce loss even further. In conventionalstate-of-the-art solid silica fibers, attenuation is dominated byRayleigh scattering and multi-phonon absorption at short and longwavelengths, respectively, resulting in an attenuation minimum at around1550 nm. In hollow-core PBG fibres most of the light does not travel inglass, and therefore the effects of Rayleigh scattering and multi-phononabsorption in the bulk material are significantly reduced, while theinternal surfaces of the fiber become a potentially much more importantcontributor to loss. Theoretical considerations indicate that theattenuation due to mode coupling and scattering at the internalair/glass interfaces, which dominate the loss in the fiber reported,should scale with the wavelength λ as λ⁻³. This was confirmed by theempirical data showing the minimum loss of hollow-core PBG fibresdesigned for various operating wavelengths in a wavelength range whereIR absorption is negligible. It is likely that silica hollow-core PBGfibres will achieve their lowest loss somewhere in the 1800-2000 nmwavelength range, well beyond the wavelength at which bulk silicaassumes its minimum loss. An alternative kind of PBG fibre, which doesnot have a cladding comprising a lattice of high and low refractiveindex regions, is described in WO00/22466. These PBG fibres typicallycomprise, in a transverse cross section, concentric, increasingly large,annuli of varying high and low refractive index material, which createan omni-directional reflector capable of confining light to a coreregion of the fibre.

PBG fibre structures are typically fabricated by first forming apre-form and then heating and drawing an optical fibre from thatpre-form in a fibre-drawing tower. It is known either to construct apre-form by stacking capillaries and fusing the capillaries into theappropriate configuration of pre-form, or to use extrusion.

For example, in PCT/GB00/01249, identified above, a seven-cell coredefect pre-form structure was formed by omitting from a stack ofcapillaries an inner capillary and, in addition, the six capillariessurrounding the inner capillary. The capillaries around the core defectboundary in the stack were supported during formation of the pre-form byinserting truncated capillaries, which did not meet in the middle of thestack, at both ends of the capillary stack. The stack was then heated inorder to fuse the capillaries together into a pre-form suitable fordrawing into an optical fibre. Clearly, only the fibre drawn from thecentral portion of the stack, with the missing inner seven capillaries,was suitable for use as a hollow core defect fibre.

US patent application number U.S. Pat. No. 6,444,133 (Corning, Inc.),describes a technique of forming a PBG fibre pre-form comprising a stackof hexagonal capillaries in which the inner capillary is missing, thusforming a core defect of the eventual PBG fibre structure that has flatinner surfaces. In contrast, the holes in the capillaries are round.U.S. Pat. No. 6,444,133 proposes that, by etching the entire pre-form,the flat surfaces of the core defect dissolve away more quickly than thecurved surfaces of the outer capillaries. The effect of etching is thatthe edges of the capillaries that are next to the central defect fullydissolve, while the remaining capillaries simply experience an increasein hole-diameter. Overall, the resulting pre-form has a greater fractionof air in the cladding structure and a core defect that is closer to aseven-cell core defect than a single cell core defect.

PCT patent application number WO 02/084347 (Corning, Inc.) describes amethod of making a pre-form comprising a stack of hexagonal capillariesof which the inner capillaries are preferentially etched by exposure toan etching agent. Each capillary has a hexagonal outer boundary and acircular inner boundary. The result of the etching step is that thecentres of the edges of the hexagonal capillaries around the centralregion dissolve more quickly than the comers, thereby causing formationof a core defect. In some examples, the circular holes are offset in theinner hexagonal capillaries of the stack so that each capillary has awall that is thinner than its opposite wall. These capillaries arearranged in the stack so that their thinner walls point towards thecentre of the structure. An etching step, in effect, preferentiallyetches the thinner walls first, thereby forming a seven-cell coredefect.

In arriving at the present invention, the inventors have appreciated anddemonstrated that, while the size of a core defect is significant indetermining certain characteristics of a PBG waveguide, the form of aboundary at the interface between core and cladding also plays asignificant role in determining certain characteristics of thewaveguide. By way of example, as will be described in detail hereafter,the inventors have shown that, for given PBG core and claddingstructures, variations in only the thickness of the boundary, at theinterface between the core and cladding, can cause significant changesin the characteristics of a respective waveguide.

According to a first aspect, the present invention provides an opticalwaveguide, comprising:

a core, comprising an elongate region of relatively low refractiveindex;

a photonic bandgap structure arranged to provide a photonic bandgap overa range of wavelengths of light including an operating wavelength oflight, the structure, in a transverse cross section of the waveguide,surrounding the core and comprising elongate relatively low refractiveindex regions interspersed with elongate relatively high refractiveindex regions; and

a relatively high refractive index boundary at the interface between thecore defect and the photonic bandgap structure, the boundary having athickness around the core such that the boundary is substantiallyanti-resonant at the operating wavelength of light.

It has been widely reported that light may be guided in a PBG fibre byvirtue of a cladding which provides a PBG. It has also been reported byLitchinitser et al., Opt Lett., Vol. 27 (2002) pp. 1592-1594, that lightmay be guided in a PBG-like fibre predominantly by anti-resonantreflection in multiple cladding layers, similar to the aforementionedconcentric structure. Litchinitser et al. describe a fibre structurecomprising a low index core surrounded by plural concentric layers ofhigh and low index material, the relative thicknesses of which werechosen to provide an anti-resonant cladding structure for confininglight to the core region. Litchinitser et al. also disclose a fibrestructure consisting of a silica core surrounded by holes filled withhigh index liquid. In that case the silica represents the low indexmedium and the filled holes are the features that act as resonators. Itwas suggested that, at their anti-resonant wavelengths, the filled holescould substantially exclude light and thus confine light to therelatively low-index silica core. It was also stated that numericalsimulations on such a structure were very time consuming and so thestudy was limited to the concentric ring structure.

In order to understand the effects of resonance and anti-resonance inoptical structures it is instructive to first consider a simple exampleof an optical resonator such as a Fabry-Perot interferometer. Whether ornot light can resonate in such a feature depends on the feature's size,shape and composition, and also on the wavelength and direction ofpropagation of the light. As the wavelength is varied the feature movesinto and out of resonance. For a given excitation, on resonance, theoptical power in the features assumes a maximum. In between resonances,optical power in the features is minimised. If the relatively lowrefractive index regions are air, it is desirable to maximise the amountof light in these regions in order to reduce scattering, non-linearitiesand other deleterious effects. That is advantageous as it raises theproportion of light in the low-index regions and decreases F-factor(described hereinafter), which is a measure of the amount of light atglass/air interfaces. Hence it is advantageous to incorporate featuresthat possess strong distinct resonances, and adjust their sizes andshapes so that they are anti-resonant at the optical wavelengths anddirections of propagation of interest.

The present inventors have discovered that confinement of light to acore of a PBG fibre, which confines light to the core region by virtueof a photonic bandgap, may be enhanced by providing, at the interfacebetween the core and the photonic bandgap cladding, a boundary which istuned to be substantially anti-resonant. Unlike in Litchinitser et al.,in which anti-resonance is achieved using concentric layers of materialor distinct, unconnected resonators, a core boundary proposed herein maycomprises a single, unbroken region of relatively high refractive indexat the interface between the core and the photonic bandgap structure.The present inventors have discovered that such a core boundary can bearranged to be anti-resonant at an operating wavelength, and therebyserve to confine light to the core of the waveguide. The presentinventors have also discovered that it is possible to achieve a similarconfinement of light to a core by arranging plural anti-resonantfeatures around an unbroken, but otherwise generally non-anti-resonant,core boundary. This latter kind of confinement, while being closelyrelated to the former kind, is described more fully in applicantsco-pending International Patent Application entitled “Improvements inand relating to optical waveguides”, having the same filing date andearliest priority date as the present application (the entire teachingof that application is hereby incorporated herein by reference).

The boundary may have a different structure from the structure of therest of the photonic band-gap structure. For example, boundary maycomprise thicker or thinner regions than those corresponding to regionsin the rest of the structure. The regions of relatively high refractiveindex may include nodes that are in different positions or havedifferent sizes from corresponding features in the rest of thestructure. The boundary may comprise, or include a region of, adifferent refractive index than the relatively high refractive indexregions in the photonic band-gap cladding structure.

Considering, for example, an air-core and silica PBG fibre, theinventors have determined that the geometry of the region of theboundary between the air core and the photonic bandgap claddingstructure has profound effects on the modal properties of the fibre. Inparticular, the inventors have appreciated that the number of guidingmodes within the band gap, the fraction of the light power of the guidedmodes confined within the air core and the field intensity of thesemodes at the air-silica interfaces all vary sensitively with thegeometry within the region. In particular, the inventors have shownthat, by tailoring the geometry, the properties of an LP₀₁-like mode(when present), which possesses an approximately Gaussian intensityprofile towards the centre of the core, can be tailored so that up toand even over 99% of the light is confined within air, and predominantlyin the core. This implies that loss due to Rayleigh scattering in thesilica may be suppressed by up to two orders of magnitude and thatnonlinearity may be substantially reduced compared with standard indexguiding single mode fibre. Also, the inventors have demonstrated thatthe core boundary geometry can be designed to reduce the field intensityof this mode strongly in the vicinity of the air-silica interfaces. Thishas the effect of reducing both the small scale interface roughnessscattering, which is discussed in detail hereafter, and the modecoupling due to longer range fibre variations.

The inventors have determined that the design of a core-claddinginterface, or boundary region, can exploit an anti-resonance effect tostrongly enhance the power in air fraction, η, and reduce the fieldintensity at the air-silica interfaces of core-guided modes, such as theLP₀₁-like mode. As has already been stated, the inventors have foundthat the geometry giving rise to the anti-resonance can be based eitheron a continuous silica boundary layer encircling the air core, such asin the example shown in FIG. 1, or on a number of localised regions ofsilica existing around the core boundary, such as in the example shownin FIG. 2.

Antiresonant boundaries have also been found, in at least someembodiments, to have the benefit of reducing the effects of, or evenremoving, so-called surface modes that can exist at a core boundary andpotentially interfere with the core-guided modes. This is particularlysurprising given that, as already mentioned, the respective coreboundaries do not typically match the form of the cladding.

The inventors suggest that the mechanism by which an anti-resonance of acontinuous core surround can occur may be understood by considering acircular tube of silica of constant thickness t and mean radius R, ofthe inner and outer silica/air interfaces, surrounded by air, as shownin FIG. 3. The properties of this system can be analysed exactly byexpressing the fields in regions I, II and III in terms of Besselfunctions using known techniques. The cylindrical symmetry implies thatmodes decouple according to an integer m, which governs the azimuthalvariation of the fields around the tube. An eigenvalue equation for eachm may be generated by applying electromagnetic boundary conditions atthe dielectric interfaces and the guiding and leaky modes of thestructure may be readily obtained from the solutions to the eigenvalueequations. The guided modes, which are concentrated in the silica,satisfy Re[β]>ω/c , Im[β]=0. The leaky modes require analyticcontinuation to complex β values; only solutions which possess smallimaginary β components are retained. At low values of m, Re[β]≈ω/c forthe leaky mode solutions and lies close to and just below the airlight-line value Re[β]<ω/c. At high values of m, low loss leaky“whispering gallery” modes, concentrated in or near the core boundary,can exist further from the light line in rings of sufficiently largeradius and thickness.

The leaky air modes can be labelled in an analogous way to the guidedmodes of standard index guiding optical fibres. Of particular interestis the LP₀₁-like leaky mode, which is the analogue of the fundamentalmode of a standard telecommunications fibre. The LP₀₁-like mode is foundto have a concentration of light power within the central hole of thetube and has an approximately Gaussian field intensity profile close tothe centre of the hole. The P-value of this mode lies close to the airlight line, so that the air-silica interfaces act as strong reflectorsof the light. This gives rise to strong confinement, as evidenced by thesmall value of Im[β] associated with the mode. The LP₀₁-like leaky modeconfinement, for a given tube radius R, is found to be stronglydependent upon the thickness t.

FIGS. 4 a and 4 b respectively show the linear and logged dependence ofIm[β] on tube wall thickness t, for mean tube radii of 6 μm and 9 μm andan operating wavelength λ=1.55 μm. A tube radius of 6 μm is close insize to the core radius of a seven-cell core defect fibre describedherein and a tube radius of 9 μm is close in size to the core radius ofa nineteen-cell core defect fibre described herein, when both areconfigured to guide light at 1.55 μm. The broad minimum occurring aroundt=0.4 μm, which is most apparent on the linear plot in FIG. 4 a, isbelieved to be due to an anti-resonance phenomenon. Clearly, the minimumis significantly lower for the 9 μm tube, which indicates that thelarger diameter tube is better able to confine light at this wavelengthto the core. Destructive interference occurs for (Hankel) waves whichare multiply reflected at the dielectric interfaces. The round-tripphase accumulated by a wave that emanates from the inner interface,propagates outwards to the outer interface, reflects and propagatesinwards to the inner interface and is again reflected, is close to π.More generally, anti-resonances occur around thickness values givingrise to a round-trip phase given by (2n+1)π, where n is an integersatisfying n≧0. For example, in a silica and air system, for tube radiisatisfying R>>λ (where λ is the operating wavelength), the thickness twhich gives rise to anti-resonance is determined from $\begin{matrix}{{t = {\frac{\lambda}{4\sqrt{n_{sil}^{2} - 1}}\left( {{2n} + 1} \right)}},} & (1)\end{matrix}$where n_(sil) is the refractive index of silica. As can be seen, t isindependent of the radius R. In this regime, the boundaries are actingas locally planar interfaces. More generally still, anti-resonances liebetween resonances, which in this case occur at $\begin{matrix}{{t \approx {\frac{\lambda}{4\sqrt{n_{sil}^{2} - 1}}2n}},{n \geq 1.}} & (2)\end{matrix}$where n is an integer. At resonances, the field is maximised within thesilica of the tube.

Equations (1) and (2), relate specifically to silica and air systems,although they can be generalised to describe other material and airsystems by replacing n_(sil) with the refractive index of the respectivematerial. Clearly, the position and scale of the graph in FIG. 4, andrespective thickness values for resonance and anti-resonance, vary asthe material refractive index and operating wavelength vary. Forexample, as the material refractive index increases, the curve in FIG. 4would contract and shift to the left; with respective thickness valuesdecreasing. Conversely, if the operating wavelength increases, the curvein FIG. 4 would expand and shift to the right; with respective thicknessvalues increasing.

The equations can be generalised for two materials having respectiverefractive indices n_(HI), and n_(LO), according to $\begin{matrix}{t = {\frac{\lambda}{4\sqrt{n_{HI}^{2} - n_{LO}^{2}}}\left( {{2n} + 1} \right)}} & (3)\end{matrix}$for anti-resonance and, for resonance $\begin{matrix}{{t \approx {\frac{\lambda}{4\sqrt{n_{HI}^{2} - n_{LO}^{2}}}\left( {2n} \right)}},{n \geq 1}} & (4)\end{matrix}$

In this case, it will be appreciated that the equations depend on bothn_(HI) and n_(LO), rather than the relatively high refractive indexalone. The skilled person will appreciate that equations (3) and (4) maybe modified to describe resonance and anti-resonance in systems wherethe tube comprises plural concentric constituent layers, or shells, forexample a high refractive index outer shell and a lower refractive indexinner shell. Such a structure may be useful for tuning the reflectivityof the inner or outer surface of the overall tube, for example, in orderto equalise the reflectivities of the tube surfaces incident with coreand cladding regions. Even more complex structures than this areenvisaged. The skilled person will be able, if required, to adapt theforegoing equations to describe the resonance and anti-resonanceproperties of such structures.

In some embodiments of the present invention, the operating wavelengthmay be at or near 1550 nm. The operating wavelength may be lower, forexample at or near to 800 nm, 1060 nm or 1300 nm. Alternatively, theoperating wavelength may be higher, for example in the range 1800nm-2000 nm, in the range 2-5 μm (for example, for mid IR spectroscopy),or even at or near 10.6 μm (for example, for transmitting light from aCO₂ laser).

Silica glass is not so optically transparent at wavelengths of lightabove about 2 μm. For transmission at the longer wavelengths, therefore,it would be preferable to use a material that is optically transparentat the wavelengths of interest. Typically, glasses such as chalcogenidesor tellurite, can have refractive indices in the region of 2.4 and aboveand can be optically transparent at wavelengths above 2 μm. Of course,use of such high index glasses has a significant impact on Equations(1)-(4), and waveguide core boundary structures would need to be scaledaccording to the equations to be anti-resonant.

FIG. 5 shows the mode field intensity I of the LP₀₁-like leaky mode fora tube with mean radius R=6 μm, thickness t=0.392 μm and wavelength 1.55μm, which corresponds to the exact anti-resonance minimum. Of course, tobenefit from anti-resonance, it is not necessary to operate at exactanti-resonance. Indeed, there is a broad range between resonance peakswhere a waveguide benefits from a boundary tuned to have some degree ofanti-resonance. It can be seen that a near null appears very close tothe inner dielectric interface and that the intensity at the outerinterface is 22 dB lower than the intensity at the centre of the hole.This field suppression at the interfaces is a feature of anti-resonance.Exploitation of the anti-resonance phenomenon both maximises theconfinement of the LP01-like leaky mode and largely minimises the fieldat the boundaries and hence the interface roughness scattering(discussed below). Of course, any well-confined, leaky mode in the core,for example a TE₀₁-like mode, would benefit in the same way as theLP₀₁-like mode.

FIG. 6 shows plots of the mode spectra of an anti-resonant tube ofradius R=6 μm and t=0.392 μm, including all guided modes and leaky modeswithin Δβ=0.15 μm⁻¹ of the air light line at λ=1.55 μm (i.e. atβ=2π/1.55), and compares it with the spectrum for a thinner silica ringof thickness t=0.1 μm, which is the approximate thickness of a claddingstructure vein according to a preferred structure, as describedhereinafter. This range of P is chosen to correspond to the band-gapwidth of a typical PBG fibre cladding. It is seen that within thisregion, the thicker anti-resonant tube actually possesses a smallernumber of modes than the thinner one. The interface field intensityreduction and the mode number reduction implies that mode couplingeffects, due to fluctuations on a length scale exceeding about 20 μm,can be expected to be lower for a thicker anti-resonant boundary than athinner one.

The inventors have applied the foregoing principles to a numericalinvestigation of continuous core surrounds, or boundaries, having shapesthat are more easily fabricated in practice, for example a dodecagonalboundary as shown in FIG. 7. The results are compared herein with thecircular geometry.

At least initially, the boundary may be considered in the absence of anycladding material; it is taken to be bounded by air. The dodecagonalboundary, which is a natural core surround shape in PBG fibresmanufactured using stacked silica tubes, as will be describedhereinafter, is found to possess a LP₀₁-like leaky mode which shows ananti-resonance effect almost identical with that of a circular tube ofthe same mean radius. The confinement of this mode is found to be onlyvery slightly compromised by the sharp comers associated with thisgeometry. A near null of the field intensity again occurs very close tothe inner dielectric interface. The thickness at anti-resonance of thisshape is very close to that of the circular tube. The number of guidedand leaky modes of this shape at anti-resonance is found to be similarto that of the tube over the PBG region, although modes possessingfaster azimuthal variation (high effective m) are shifted significantlyby the change in geometry and the confinement of leaky modes with higheffective m is reduced by the appearance of comers.

The inventors have considered full PBG fibre geometries, as shown inFIGS. 8 a and 8 b, with band gap cladding material surrounding acontinuous core boundary. It is found that the anti-resonance phenomenonassociated with the continuous core surround occurs for these structuresalso. This is evidenced by scanning over boundary thickness t andnumerically calculating the LP₀₁-like mode solutions.

As a function of t, broad maxima in the fraction η of the light power inair are observed, together with broad minima in F-factor (describedbelow), which measures field intensity at the dielectric interfaces andgives a direct relative measure of the strength of small scale interfaceroughness scattering and provides an indication of the relative strengthof mode coupling effects due to longer scale fluctuations.

In fact, the thickness for anti-resonance for the core surround boundedby air can be used as an indication of the boundary thickness requiredfor anti-resonance in the PBG fibre geometry, as will be demonstrated.The thickness t at anti-resonance for the latter geometry is found to bea little lower than for the former one. This difference is believed tobe a function of the silica associated with the PBG cladding structure,which connects onto the outer surface of the boundary. In other words,the boundary has an ‘effective thickness’, which is typically greaterthan the actual thickness, where effective thickness will vary dependingon the form of the cladding which meets the outer surface of theboundary. Furthermore, examination of the mode field intensity of theLP₀₁-like mode shows that near nulls appear close to the inner surfaceof the boundary in the PBG fibre at maximum η and minimum F-factor, justas they do for the core surround in air at anti-resonance. This confirmsthe anti-resonance mechanism for PBG fibre geometry. Hence, F-factor, ηand anti-resonance are proxies for one another in that determining anyone provides specific information about the other two.

According to a second aspect, the present invention provides an opticalwaveguide, comprising:

a core, comprising an elongate region of relatively low refractiveindex;

a photonic bandgap structure arranged to provide a photonic bandgap overa range of wavelengths of light, the structure, in a transverse crosssection of the waveguide, surrounding the core and comprising elongaterelatively low refractive index regions interspersed with elongaterelatively high refractive index regions; and

a relatively high refractive index boundary at the interface between thecore defect and the photonic bandgap structure, the boundary having athickness around the core such that, in use, light guided by thewaveguide is guided in a transverse mode in which, in the transversecross-section, more than 95% of the guided light is in the regions ofrelatively low refractive index in the waveguide.

As indicated, guiding light in a region of relatively low refractiveindex has the advantage that losses, nonlinear effects and othermaterial effects are generally lower in such regions, particularly ifthe region is a region of air or a gas. Thus, preferably in thetransverse cross-section, ever more of the light may be guided in theregions of relatively low refractive index in the PBG structure and thecore: preferably more than 96%, 97%, 98%, 99%, 99.3%, 99.5% or even99.9% of the light is in those regions.

The boundary may have a thickness such that, in use, light guided by thewaveguide is guided in a transverse mode in which, in the transversecross-section, more than 50% of the guided light is in the region ofrelatively low refractive index in the core. It is significant that theinventors have recognised that the light need not be in the core regionfor beneficial effects to be achieved. Thus, the boundary may have ashape such that, in use, light guided by the waveguide is guided in atransverse mode in which, in the transverse cross-section, more than 1%of the guided light is in the regions of relatively low refractive indexin the photonic bandgap structure. It may be that still more of theguided light is in those regions in the PBG structure: more than 2%,more than 5% or even more than 10% of the light may be in those regions.

The boundary may have a thickness such that, in use, light guided by thewaveguide is guided in a transverse mode providing an F-factor of lessthan 0.23 μm⁻¹ for an operating wavelength of 1.55 μm, less than anequivalent F-factor value scaled for a different operating wavelength(given by the formula F=0.23*(1.55/(λ/μm⁻¹))/μm⁻¹, where λ is theoperating wavelength) or less than 0.7 Λ⁻¹ for structures having aperiodic cladding with a pitch Λ.

F-factor has been identified by the present inventors as a useful figureof merit which relates to how the guided light propagating in a PBGfibre is subject to scattering from small scale irregularities of theair-silica interfaces. F-factor is also believed to be a strongindicator of likely mode-coupling characteristics of a PBG-fibre. Therelevant F-factor is typically the F-factor only of the mode of interest(for example, the fundamental mode, ignoring higher-order modes).

Scattering due to small scale irregularities acts in addition to theRayleigh scattering due to index inhomogeneity within silica, or anyother such optical guiding medium. The latter loss mechanism is stronglysuppressed in air-core PBG fibres, if most of the light power is in air.It remains to ascertain the limit that hole interface scattering placeson loss, given that some interface roughness is always present. Theamount of scattering associated with air-silica boundaries can beminimised by ensuring that impurities are eliminated during the drawprocess; such impurities can act as scattering (and absorption) centresdirectly, and can operate as nucleation sites for crystallite formation.With these imperfections removed, there still remains interfaceroughness governed by the thermodynamics of the drawing process. Theinventors believe that such fluctuations are likely to be difficult orimpossible to remove altogether.

The Rayleigh scattering due to small scale roughness at the air-silicainterfaces may be calculated by applying a perturbation calculation. Theanalysis has a simple interpretation in terms of effective particulatescatterers distributed on the interfaces. If the root-mean square (RMS)height roughness is h_(rms) and the correlation lengths of the roughnessalong the hole direction and around the hole perimeter are L_(z) andL_(Φ) respectively, then a typical scatterer has a volumeh_(rms)L_(z)L_(Φ). The induced dipole moment of the typical scatterer isthen given byp=ΔεΕ₀h_(rms)L_(z)L_(Φ)  (5)where Δε is the difference in dielectric constant between silica andair, and Ε₀ is the E-field strength at the scatterer. This induceddipole moment radiates a power, in the free space approximation, givenby $\begin{matrix}{P_{sc} = {{\frac{1}{12\pi}\left( \frac{\omega}{c} \right)^{4}\left( \frac{ɛ_{0}}{\mu_{0}} \right)^{1/2}{p}^{2}} = {\frac{1}{12\pi}\left( \frac{\omega}{c} \right)^{4}{\Delta ɛ}^{2}h_{rms}^{2}L_{z}^{2}{L_{\phi}^{2}\left( \frac{ɛ_{0}}{\mu_{0}} \right)}^{1/2}{{E_{0}}^{2}.}}}} & (6)\end{matrix}$

The number density of particles on the interface will be ˜1/(L_(z)L_(Φ))so that the total radiated power from a section of length L of theperturbed fibre will be approximately $\begin{matrix}{P_{rad} \sim {\frac{1}{12\pi}\left( \frac{\omega}{c} \right)^{4}{\Delta ɛ}^{2}h_{rms}^{2}L_{z}L_{\phi}{L\left( \frac{ɛ_{0}}{\mu_{0}} \right)}^{1/2}{\oint_{\underset{perimeters}{pole}}{{\mathbb{d}s}{E_{0}}^{2}}}}} & (7)\end{matrix}$

The loss rate is thus given by $\begin{matrix}{\gamma = {\frac{P_{rad}}{P_{0}L} \sim {\frac{1}{6\pi}\left( \frac{\omega}{c} \right)^{4}{\Delta ɛ}^{2}h_{rms}^{2}L_{z}{L_{\phi}\left( \frac{ɛ_{0}}{\mu_{0}} \right)}^{1/2}\frac{\oint_{\underset{perimeters}{pole}}{{\mathbb{d}s}{E_{0}}^{2}}}{\int{{\mathbb{d}{S\left( {E_{0}\bigwedge H_{0}^{*}} \right)}} \cdot \hat{z}}}}}} & (8)\end{matrix}$where the incident power P₀ has been expressed as a Poynting flux.

Equation (8) shows that the mode shape dependence of the Rayleighinterface roughness scattering strength is governed by an F-factor,given by $\begin{matrix}{F = {\left( \frac{ɛ_{0}}{\mu_{0}} \right)^{1/2}\frac{\oint_{\underset{perimeters}{pole}}{{\mathbb{d}s}{{E_{0}\left( r^{\prime} \right)}}^{2}}}{\int_{x - {section}}{{\mathbb{d}{S\left( {E_{0}\bigwedge H_{0}^{*}} \right)}} \cdot \hat{z}}}}} & (9)\end{matrix}$

The inventors have found that a comparison of the interface scatteringstrength from guided modes of different fibres with similar interfaceroughness properties can be based purely on the F-factor. Indeed, thethermodynamic limit to surface roughness is not expected to vary greatlywith small variations in the fibre geometry, so that the F-factor can beused directly as a figure of merit for any fibre which has interfaceswhich cause scattering and contribute to loss.

According to a third aspect, the present invention provides an opticalwaveguide, comprising:

a core, comprising an elongate region of relatively low refractiveindex;

a photonic bandgap structure arranged to provide a photonic bandgap overa range of wavelengths of light, the structure, in a transverse crosssection of the waveguide, surrounding the core and comprising elongaterelatively low refractive index regions interspersed with elongaterelatively high refractive index regions; and

a relatively high refractive index boundary at the interface between thecore defect and the photonic bandgap structure, the boundary having athickness around the core such that, in use, light guided by thewaveguide is guided in a transverse mode providing an F-factor of lessthan 0.231 μm⁻¹ for an operating wavelength of 1.55 μm, less than anequivalent F-factor value scaled for a different operating wavelength orless than 0.7 Λ⁻¹ for structures having a periodic cladding and a pitchΛ.

Preferably, for any of the aforementioned waveguides, still lowerF-factors are provided: less than 0.17 μm⁻¹, less than 0.1 μm⁻¹, lessthan 0.07 μm⁻¹, less than 0.06 μm⁻¹, less than 0.05 μm⁻¹, less than0.033 μm⁻¹, less than 0.03 μm⁻¹, less than 0.027 μm⁻¹, less than 0.023μm⁻¹, less than 0.02 μm⁻¹, less than 0.017 μm⁻¹, less than 0.013 μm⁻¹,less than 0.01 μm⁻¹, less than 0.0067 μm⁻¹, or even less than 0.0033μm⁻¹ are preferred (for an operating wavelength of 1.55 μm, (orequivalent scaled values for an alternative operating wavelength)—for aPBG fibre that has a periodic photonic bandgap structure, with a pitchΛ, these values scale inversely with pitch and become less than 0.5 Λ⁻¹,less than 0.3 Λ⁻¹, less than 0.2 Λ⁻¹, less than 0.17 Λ⁻¹, less than 0.15Λ⁻¹, less than 0.01 Λ⁻¹, less than 0.09 Λ⁻¹, less than 0.08 Λ⁻¹, lessthan 0.07 Λ⁻¹, less than 0.06 Λ⁻¹ less than 0.05 Λ⁻¹, less than 0.04Λ⁻¹, less than 0.03 Λ⁻¹, less than 0.02 Λ⁻¹, or even less than 0.01 Λ⁻¹respectively. As has already been described, anti-resonance strength canbe stronger for larger diameter core radii. Accordingly, core radius maybe varied to meet a required F-factor; where increased radius alsoenables decreased F-factor.

A more rigorous calculation of small scale interface roughness can bederived which takes into account the details of the surface roughnessspectrum and deviations from the free space approximation. The lattereffect is embodied by a local density of states (LDOS) correction factorappearing in the integrand of the numerator integral in equation (9).Ideally, to minimise the interface loss, the field intensity of theguiding mode multiplied by the LDOS factor should be maintained as smallpossible at the interfaces. In practise, the LDOS correction is found tobe small even for (silica/air) PBG fibres in comparison with the guidedmode field intensity factor; so that the F-factor given in equation (9)may be used to compare the interface scattering strength from guidedmodes of different fibre designs.

The effect of the scattering from crystallites which have formed closeto the air/silica interfaces can be calculated in a similar way to thegeometrical roughness considered above. Assuming the number density perunit interface length and the size of the crystallites is independent offibre design, again F-factor can be used directly to compare theinterface scattering strengths.

The features next discussed may be found in embodiments of any one ofthe preceding three aspects of the invention (relating toanti-resonance, proportion η of light in the relatively low refractiveindex regions or F-factor).

According to the second aspect of the invention, the boundary may beanti-resonant at an operating wavelength of light. Additionally, oralternatively, the boundary may be a reflector.

The boundary may have a substantially constant thickness around thecore. Alternatively, the boundary may have a thickness that variesaround the core. In either case, thickness variations at points wherethe cladding joins the boundary may be ignored for the purposes ofsimplified analysis. The boundary may have a thickness that variesperiodically around the core.

For core boundaries that vary in thickness, the core boundary may have athickness t around a proportion y of the boundary, where y>0.5. Indeed,y may be greater than 0.6, 0.7, 0.8, 0.9 or be substantially equal to1.0.

In the transverse cross section, the photonic bandgap structure maycomprise an array of the relatively low refractive index regionsseparated from one another by the relatively high refractive indexregions. The array may be substantially periodic. Of course, the arrayneed not be periodic, as described in the aforementioned paper by N. M.Litchinitser et al.

It is highly unlikely in practice that a photonic bandgap structureaccording to the present invention will comprise a ‘perfectly’ periodicarray, due to imperfections being systematically or accidentallyintroduced into the structure during its manufacture and/orperturbations being introduced into the array by virtue of the presenceof the core defect and/or boundary region. The present invention isintended to encompass both perfect and (purposely or accidentally)imperfect structures. Likewise, any reference to “periodic”, “lattice”,or the like herein, imports the likelihood of imperfection.

The array may be a substantially triangular array. Other arrays, ofcourse, may be used, for example, square, hexagonal or Kagomé, to namejust three.

The boundary region may comprise, in the transverse cross-section, aplurality of relatively high refractive index boundary veins joinedend-to-end around the boundary between boundary nodes, each boundaryvein being joined between a leading boundary node and a followingboundary node, and each boundary node being joined between two boundaryveins and to a relatively high refractive index region of the photonicbandgap structure.

At least some of the boundary veins may be substantially straight. Insome embodiments, substantially all of the boundary veins aresubstantially straight. Alternatively, or additionally, at least some ofthe boundary veins may be bowed outwardly from, or inwardly towards, thecore defect.

At least two of the higher index regions in the photonic bandgapstructure may be connected to each other. Indeed, the higher indexregions in the photonic bandgap structure may be interconnected.

The photonic bandgap structure may comprise an arrangement of isolatedrelatively low refractive index regions separated by connected regionsof relatively high refractive index. The connected regions of relativelyhigh refractive index may comprise an array of veins, each vein beingconnected at each end thereof to a node, which, in turn, is connected toat least two other veins. The arrangement of nodes and veins may varyfrom this at the inner or outer periphery of the photonic band-gapstructure. Each vein may have a characteristic thickness substantiallyat its mid-point between the two nodes to which it is connected.

The boundary may comprise, in the transverse cross-section, a pluralityof relatively high refractive index boundary veins connected end-to-endaround the boundary between neighbouring boundary nodes (with nointermediate boundary nodes), each boundary vein being connected betweena leading boundary node and a following boundary node, and each boundarynode being connected between two boundary veins and to a relatively highrefractive index region of the photonic bandgap structure. Then, eachboundary vein may have a characteristic thickness substantially at themid-point between the two boundary nodes to which it is connected.Preferably, more than a half of the boundary veins have a characteristicthickness at their mid-points, which is substantially the thinnestregion along the vein.

It will be appreciated that, in practical fibres, it is difficult tocontrol the fabrication process to achieve exact dimensions, forexample, of core boundary thickness. However, as already indicated, theanti-resonance minima are quite broad, compared with resonances, whichare characterised by sharp peaks at certain thicknesses of coreboundary. Thus, a core boundary thickness in the region of ananti-resonance minimum, even if not exactly at the minimum, will stillprovide an advantage over other waveguides.

The characteristic thickness of at least one boundary vein may be atleast 110% of the characteristic thickness of a plurality of the veinsin the array of veins in the photonic band-gap structure. For example,the characteristic thickness of a plurality of the boundary veins may beat least 110% of the characteristic thickness of a plurality of theveins in the array of veins in the photonic band-gap structure. Indeed,the characteristic thickness of at least a majority of the boundaryveins may be at least 110% of the characteristic thickness of at least amajority of the veins in the array of veins in the photonic band-gapstructure.

In any event, the aforementioned boundary vein or veins may be eventhicker than the aforementioned veins in the photonic band-gapstructure. For example, the boundary vein or veins may be at least 120%,140%, 160% or 180% of the characteristic thickness of the respectivecladding veins. The boundary veins may be thicker still, for example,they may be at least 200%, 220%, 240% or even thicker than thecharacteristic thickness of the respective cladding veins.

In some embodiments of the present invention, substantially all of theboundary veins are thicker than substantially all of the veins in thephotonic band-gap structure.

The boundary veins may be thinner than the veins in the photonicband-gap structure. The boundary vein or veins may be at most 90%, 80%,60%, 40% or even thinner than the characteristic thickness of therespective cladding veins.

The array may have a characteristic primitive unit cell and a pitch Λ.For example, the pitch may be between 3 μm and 6 μm.

In a waveguide in which the photonic band-gap cladding is periodic andhas a characteristic pitch Λ, the core boundary thickness may beexpressed as a proportion of the pitch. For example, the boundary mayhave a thickness t, wherein, t=uΛ for a proportion of the boundary y,where u>0.06 and y>0.5. For example, u may be even greater, for exampleu>0.05, 0.07, 0.09, 0.1, or 0.11. Additionally, or alternatively, y maybe greater, for example y>0.6, 0.7, 0.8, 0.9 or may be substantiallyequal to 1.0.

Generally, as already described with reference to Equation (3), indetermining whether a core boundary is anti-resonant, it is necessary toconsider the operating wavelength of the waveguide and the refractiveindex contrast between the relatively high refractive index regions andthe relatively low refractive index regions. Hence, it may be foundconvenient to express the core boundary thickness in terms of Equation(3). For example, the core boundary thickness may be characterised by taccording to:$\frac{a\quad\lambda}{4\sqrt{n_{HI}^{2} - n_{LO}^{2}}} \leq t \leq \frac{b\quad\lambda}{4\sqrt{n_{HI}^{2} - n_{LO}^{2}}}$where a=0.5 and b=1.75 and n_(HI) and n_(LOW) are the refractive indicesof the core surround and of the material within the core, respectively.Clearly, this range of thickness values is below the first-orderresonance peak (m=1), which has be shown to lie at around t=0.74 μm forthe aforementioned silica example. It is unlikely that core boundarythicknesses beyond the first-order resonance peak will find practicalapplication, since the region would be thick enough to become anefficient waveguide thus negating the possible advantages of having ananti-resonant boundary. With reference to the graphs in FIG. 4, whichrelate to the specific case of a silica and air fibre operating at awavelength of 1.55 μm, t is preferably in the approximate range 0.2 μmto 0.7 μm inclusive, and the curve has a minimum value at approximately0.4 μm. Preferably, a>0.5, for example, a may be greater than or equalto 0.6, 0.7, 0.8, 0.9 or 1.0 (and b≧a). Independently, or incombination, b<1.75, for example, b may be less than or equal to 1.7,1.6, 1.5, 1.4, 1.3, 1.2, 1.1 or 1.0 (and b≧a). It may be desirable tospecify a core boundary thickness that is to the right or left of theanti-resonant point, in which case b≧a>1.0 or a≦b<1.0 respectively. In apreferred embodiment, a>0.8 and b<1.2. In a more preferred embodiment,a>0.9 and b<1.1.

It is expected that, as fabrication processes improve, it will bepossible to make a core boundary very close to a desired thickness.There may be reasons for making a core boundary with a thickness whichis not optimum according to a strict anti-resonance analysis. Oneexemplary reason may be mode crossings, which can have deleteriouseffects of the transmission characteristics of a fibre, as will bediscussed hereinafter.

The core may have, in the transverse cross-section, an area that issignificantly greater than the area of at least some of the relativelylow refractive index regions of the photonic bandgap structure. The coremay have, in the transverse cross-section, an area that is greater thantwice the area of at least some of the relatively low refractive indexregions of the photonic bandgap structure. The core may have, in thetransverse cross-section, an area that is greater than the area of eachof the relatively low refractive index regions of the photonic bandgapstructure.

The core may have, in the transverse cross-section, a transversedimension that is greater than the pitch Λ of the photonic band-gapcladding.

The core may have a size that you would expect to obtain from theomission of a plurality of unit cells of the photonic band-gapstructure, for example, the core may correspond to the omission ofthree, four, six, seven, ten, twelve or nineteen unit cells of thephotonic band-gap structure. The core may correspond to the omission ofmore than nineteen unit cells of the photonic band-gap structure, forexample thirty-seven cells.

At least some of the relatively low refractive index regions may have arefractive index of less than 2, less than 1.8, less than 1.6, less than1.5, less than the refractive index of silica, less than 1.4, less than1.3, less than the refractive index of typical polymer glasses (forexample, less than 1.25), less than 1.2 or even less than 1.1 or evenless than 1.05, or be 1. For example, at least some of the relativelylow refractive index regions may comprise a solid material or may bevoids filled with air or under vacuum. Alternatively, at least some ofthe relatively low refractive index regions may be voids filled with aliquid or a gas other than air. The region of relatively low refractiveindex that makes up the core may comprise the same or a differentmaterial compared with the regions of relatively low refractive index inthe photonic bandgap structure.

In some embodiments, at least some of the relatively high refractiveindex regions comprise silica glass. The glass may be un-doped or dopedwith index raising or lowering dopants. As used herein ‘silica’encompasses fused silica, including doped fused silica, and silicateglasses in general such as germano-silicates and boro-silicates.

In alternative embodiments of the invention the relatively highrefractive index regions comprise a material other than silica. Forexample, it may be an inorganic glass in which multi-phonon absorptiononly becomes significant at wavelengths significantly longer than forsilica. Exemplary inorganic glasses may be in the category of halideglasses, such as a fluoride glass, for example ZBLAN. Alternatively, therelatively high refractive index may comprise another solid material,for example an organic polymer.

The relatively low refractive index regions may make up more than 75% byvolume of the photonic bandgap structure. This volume may be above 80%,for example 87.5%, or may be above 90%. Of course, in practical fibres,the photonic band-gap structure is typically surrounded by one or moreouter, over-cladding layers of material, which are typically solid anddo not factor in the preceding volume calculations.

The waveguide may support a mode having a mode profile that closelyresembles the fundamental mode of a standard optical fibre. An advantageof this is that the mode may readily couple into standard, single modeoptical fibre.

Alternatively, or in addition, the waveguide may support anon-degenerate mode. This mode may resemble a TE₀₁ mode in standardoptical fibres.

Preferably, in either case, said mode supports a maximum amount of themode power in relatively low refractive index regions compared withother modes that are supported by the waveguide.

According to a fourth aspect, the present invention provides an opticalfibre comprising a waveguide according to any of the first three aspectsof the present invention.

As will be described hereinafter, embodiments of the present inventionprovide an optical fibre, of the aforementioned kind, wherein the lossof the optical fibre may be less than 5dB/km. According to a preferredembodiment of the present invention, the loss may be less than 2 db/km.

According to a fifth aspect, the present invention provides an opticalfibre transmission system comprising a transmitter, a receiver and anoptical fibre, according to the fourth aspect of the present invention,for transmitting light between the transmitter and the receiver.

According to a sixth aspect, the present invention provides dataconditioned by having been transmitted through a waveguide ortransmission system, as described above. As in any transmission system,data that is carried by the system acquires a characteristic ‘signature’determined by a transfer function of the system. By characterising thesystem transfer function sufficiently accurately, using knowntechniques, it is possible to match a model of the input data, operatedon by the transfer function, with real data that is output (or received)from the transmission system.

Also according to the invention there is provided a method of forming anelongate waveguide, comprising the steps:

forming a preform stack by stacking a plurality of elongate elements;

omitting, or substantially removing at least one elongate element froman inner region of the stack; and

heating and drawing the stack, in one or more steps, into a waveguide ofa type described above as being according to the invention.

Also according to the invention there is provided a method of formingelongate waveguide for guiding light, comprising the steps:

simulating the waveguide in a computer model, the waveguide comprising acore, comprising an elongate region of relatively low refractive indexand a photonic bandgap structure arranged to provide a photonic bandgapover a range of wavelengths of light, the structure comprising elongateregions of relatively low refractive index interspersed with elongateregions of relatively high refractive index, including a boundary regionof relatively high refractive index that surrounds, in a transversecross-section of the waveguide, the core, wherein properties of theboundary region are represented in the computer model by parameters;

finding a set of values of the parameters that, according to the model,increases or maximises how much of the light guided by the waveguide isin the regions of relatively low refractive index in the waveguide; and

making a waveguide using the values.

Also according to the invention, there is provided a method of formingelongate waveguide for guiding light, comprising the steps:

simulating the waveguide in a computer model, the waveguide comprising acore, comprising an elongate region of relatively low refractive indexand a photonic bandgap structure arranged to provide a photonic bandgapover a range of frequencies of light, the structure comprising elongateregions of relatively low refractive index interspersed with elongateregions of relatively high refractive index, including a boundary regionof relatively high refractive index that surrounds, in a transversecross-section of the waveguide, the core wherein properties of theboundary region are represented in the computer model by parameters;

finding a set of values of the parameters that, according to the model,decreases or minimises the F-factor of the waveguide; and

making a waveguide using the values.

According to a further aspect, the present invention provides a photoniccrystal fibre, comprising:

an elongate, relatively low refractive index core;

an elongate photonic bandgap structure surrounding the core andcomprising, in the transverse cross section, a lattice of relatively lowrefractive index regions separated by connected relatively highrefractive index regions; and

a concentric boundary region, at the interface between the core and thephotonic bandgap structure, the core boundary region being generallythicker around its circumference than regions of relatively highrefractive index in the photonic bandgap structure.

According to a further aspect, the present invention provides an opticalwaveguide comprising:

a core, comprising an elongate region of relatively low refractiveindex;

an outer structure, surrounding, in a transverse cross section of thewaveguide, the core and comprising elongate relatively low refractiveindex regions interspersed with elongate relatively high refractiveindex regions; and

a relatively high refractive index boundary at the interface between thecore defect and the outer structure, the boundary having a thicknessaround the core such that the boundary is substantially anti-resonant atthe operating wavelength of light.

The outer structure may be a photonic bandgap structure. Even if theouter structure is not a photonic bandgap structure, any features setout above in relation to other aspects of the invention having a bandgapstructure may be found in the present further aspect of the inventionunless that is not physically meaningful. The waveguide may comprise ajacket around the outer structure.

Other aspects and embodiments of the present invention will becomeapparent from reading the following description and claims andconsidering the following drawings.

Embodiments of the present invention will now be described, by way ofexample only, with reference to the accompanying drawings, of which:

FIG. 1 is a diagram of a transverse cross section of a PBG fibrestructure having a generally constant thickness core boundary;

FIG. 2 is a diagram of a transverse cross section of a PBG fibrestructure having a varying thickness core boundary;

FIG. 3 is a diagram which shows in transverse cross section of acircular tube of silica in air;

FIG. 4 is a graph which shows the imaginary part of the longitudinalpropagation constant β plotted as a function of tube thickness t on (a)a linear and (b) a log. y-axis scale;

FIG. 5 is a graph which shows the radial dependence of the LP₀₁-likeleaky mode field intensity for an anti-resonant silica tube of the kindshown in FIG. 2;

FIG. 6 shows the mode spectra of silica tubes of radius R at thicknessest=0.392 μm and t=0.1 μm;

FIG. 7 is a diagram which illustrates the geometry of a dodecagonal coresurround;

FIGS. 8 a and 8 b are diagrams of transverse cross sections of PBG fibrestructures of the kind used in embodiments of the present invention,wherein the structure illustrated in FIG. 8 a has a seven-cell coredefect and the structure illustrated in FIG. 8 b has a nineteen-cellcore defect;

FIGS. 9 a and 9 b are graphs which show light power in air and F-factorrespectively for seven-cell PBG fibre structures having differentboundary thicknesses and FIG. 9 c is a graph of F-factor fornineteen-cell PBG fibre structures having different boundarythicknesses;

FIGS. 10 a and 10 b are diagrams illustrating arrangements ofcapillaries and rods used in forming waveguide structures according toembodiments of the present invention;

FIGS. 11 a and 11 b are scanning electron micrographs of a seven-cellcore defect structure and a nineteen-cell core defect structure madefrom pre-forms according to FIGS. 10 a and 10 b respectively;

FIG. 12 is a graph showing transmission loss plotted against wavelengthfor the fibre shown in transverse cross section in FIG. 11 b;

FIG. 13 is a diagram of an alternative embodiment of the presentinvention; and

FIG. 14 is a diagram of another alternative embodiment of the presentinvention.

FIG. 8 a is a representation, shown in transverse cross-section, of aninner region of a PBG fibre waveguide structure of the kind used inembodiments of the present invention. In the Figure, the black regionsrepresent fused silica glass and the white regions represent air holesin the glass. As illustrated, the cladding 100 comprises a triangulararray of generally hexagonal cells 105, surrounding a seven-cell coredefect 110. This region of the cladding, although not shown in itsentirety, typically extends outwardly to provide a specified degree oflight confinement; where more cladding layers provide increasedconfinement. Typically, although not shown, there are further claddinglayers surrounding the photonic band-gap structure. There may be anadditional solid silica layer to provide strength and a coating layer toprotect the silica and prevent light entering the fibre from the side,as in a normal fibre. A core defect boundary 145 is at the interfacebetween the cladding and the core defect. The core defect boundary hastwelve sides—alternating between six relatively longer sides 140 and sixrelatively shorter sides 130—and is formed by omitting or removing sevencentral cells—an inner cell and the six cells that surround the innercell. The cells would have typically been removed or omitted from apre-form prior to drawing the pre-form into the fibre. As the skilledperson will appreciate, although a cell comprises a void, or a hole, forexample filled with air or under vacuum, the voids or holes mayalternatively be filled with a gas or a liquid or may instead comprise asolid material that has a different refractive index than the materialthat surrounds the hole. Equally, the silica glass may be doped orreplaced by a different glass or other suitable material such as apolymer. For the sake of simplicity of description herein, however, thefollowing exemplary embodiments are silica and air fibres.

The waveguide of FIG. 8 a has a substantially periodic structure,comprising a triangular lattice of generally hexagonal holes. However,as already discussed, N. M. Litchinitser et al. have demonstrated thatphotonic bandgaps may be achieved in non-periodic structures. Theproperties of the core-cladding boundary are also important innon-periodic PBG structures and the invention is not limited tosubstantially periodic structures but encompasses structures with someor even a high degree of aperiodicity or irregularity in the claddingstructure. However, the exemplary embodiments illustrated hereafter usea triangular lattice of the kind shown in FIG. 8 a, which will befamiliar to the skilled artisan, in order not to obscure the presentinvention.

Hereafter, and with reference to FIG. 8 a, a region of glass 115 betweenany two holes is referred to as a “vein” and a region of glass 120 wherethree veins meet is referred to as a “node”. A vein can be generallycharacterised by its transverse, cross-sectional length and thickness ata midpoint between the two nodes to which it is attached. Veins tend toincrease in thickness from their midpoint to the nodes, although aregion of substantially constant thickness at the middle of the veintends to appear and then increase in length with increasing air-fillingfraction. Nodes can be generally characterised by a transversecross-sectional diameter, which is the diameter of the largest inscribedcircle that can fit within the node. In the fibre structuresinvestigated herein, node diameter is typically larger than thethickness of the veins attached to the node.

The core defect boundary 145 comprises the inwardly-facing veins of theinnermost ring of cells that surround the core defect 110.

In practice, for triangular lattice structures that have a largeair-filling fraction, for example above 85%, most of the cladding holes105 assume a generally hexagonal form, as shown in FIG. 8 a, and theveins are generally straight.

The cells forming the innermost ring around the boundary of the coredefect, which are referred to herein as “boundary cells”, have one oftwo general shapes. A first kind of boundary cell 125 is generallyhexagonal and has an innermost vein 130 that forms a relatively shorterside of the core defect boundary 145. A second kind of boundary cell 135has a generally pentagonal form and has an innermost vein 140 that formsa relatively longer side of the core defect boundary 145.

There are twelve boundary cells 125, 135 and twelve nodes 150, which arereferred to herein as “boundary nodes”, around the core defect boundary145. Specifically, as defined herein, there is a boundary node 150wherever a vein between two neighbouring boundary cells meets the coredefect boundary 145. In FIG. 8 a, these boundary nodes 150 have slightlysmaller diameters than the cladding nodes 160. For the present purposes,the veins 130 & 140 that make up the core defect boundary are known as“boundary veins”.

FIG. 8 b is a diagram of an exemplary nineteen-cell core defectstructure. Other than the size of the core defect, the structure has thesame cladding properties as the structure shown in FIG. 8 a.

In both structures, the core defect boundary 145 can be thought of as agenerally annular, constant thickness region of glass surrounding thecore region 110 and acting to provide confinement of light to the coreindependently of, but in addition to, the photonic band-gap structurethat forms the inner cladding region 100. Clearly, the boundary regionis not perfectly annular, due to it being formed from plural, generallystraight boundary veins, and is not of constant thickness, due to slightvariations in thickness along boundary veins and, in particular, atboundary nodes. However, for the present purposes herein, this kind ofcore boundary will be thought of as being generally annular and ofgenerally constant thickness.

In the prior art, photonic band-gap fibres typically comprise eitherplural concentric layers of dielectric material surrounding a core, toform an omni-directional waveguide, or a microstructured photonicband-gap cladding, comprising a triangular lattice of hexagonal holes,surrounding a core region. In the latter kind of band-gap fibre, thereis a core defect boundary but the shape and form of the boundary hastypically been a simple function or artefact of the pre-form andmanufacturing process used to make the fibre. Certainly, there are noprior art band-gap fibres of the kind presented in the exemplaryembodiments herein, in which a generally annular core boundary region,which is produced to be substantially anti-resonant, sits at theinterface between a core region and a periodic, microstructured photonicband-gap cladding structure.

The structures in FIG. 8 a and 8 b, and each of the following examplesof different structures, closely resemble practical optical fibrestructures, which have either been made or may be made according toknown processes or the processes described hereinafter. The structureshave the following characteristics in common (unless otherwise stated):

a pitch Λ of the cladding chosen between values of approximately 3 μmand 6 μm (this value may be chosen to position core-guided modes at anappropriate wavelength for a particular application);

a thickness t of the cladding veins (at their mid-points) of 0.0548times the chosen pitch λ of the cladding structure (or simply 0.0548 Λ);

an air-filling fraction in the cladding of approximately 87.5%.

Of course, smaller pitches may be chosen for fibres operating in shortwavelength regimes, for example at 800 nm or in the visible regions ofthe electromagnetic spectrum, and larger pitches may be chosen foroperation in the mid-IR spectrum or even at the CO₂ laser wavelength of10.6 μm. For longer wavelength applications, for example beyond 2 μm,the larger pitch may be used in tandem with a material other thansilica, which should be optically transparent at the respectivewavelength.

As described above, the present inventors have determined that it ispossible to control the performance of PBG fibres in particular byminimising the F-factor or maximising the amount of light thatpropagates in air within the fibre structure, even if some light is notin the core, in order to benefit from the properties of PBG fibres, suchas reduced absorption, non-linearity and, in addition, reduced modecoupling. As has been described, light in air and F-factor are proxiesto anti-resonance exhibited by the core boundary.

To this end, the inventors have analysed a significant number of, both,seven-cell and nineteen-cell core defect PBG fibres in which only thethickness of the boundary veins has been varied; from 1.4 times thethickness of the cladding veins to 2.4 times the thickness of thecladding veins, in steps of 0.1 times the thickness of the claddingveins for the seven cell defect fibres and from 0.7 times the thicknessof the cladding veins to 2.5 times the thickness of the cladding veins,in steps of 0.1 times the thickness of the cladding veins thenineteen-cell core defect fibres.

All boundary vein thicknesses are measured at their centre pointsbetween the two boundary nodes to which they are attached. It is evidentthat even relatively thick boundary veins are slightly thicker at thepoint where they meet the boundary nodes than at their mid-pointsbetween nodes. However, for the purpose of stating boundary veinthickness, the thickness of the vein at its centre is used and theslightly increased thickness of the boundary veins at their ends isignored.

The ranges of boundary thickness values sampled include the theoreticalanti-resonant point, which is somewhere between 2.1 and 2.3 times thethickness of the cladding veins (equivalent to 0.371-0.407 μm at anoperational wavelength of 1550 nm); the anti-resonant point being at anapproximate thickness of 0.4 μm according to the graphs in FIG. 4.Specific details of the seven-cell core defect structures are providedin Table 1 below. TABLE 1 Boundary vein thickness relative to: Claddingvein Cladding Operating Absolute Light power thickness (%) pitch Λwavelength λ (%) thickness (μm) in air η (%) F-factor (Λ⁻¹) 140 0.07716.0 0.248 92 1.68 150 0.082 17.1 0.266 97 0.67 160 0.088 18.3 0.283 980.38 170 0.093 19.4 0.301 98 0.34 180 0.099 20.5 0.318 99 0.23 190 0.10421.7 0.336 99 0.23 200 0.110 22.8 0.354 98 0.29 210 0.115 24.0 0.371 970.46 220 0.121 25.1 0.389 90 1.17 230 0.126 26.3 0.407 89 1.06 240 0.13227.4 0.425 95 0.57

In Table 1, boundary vein thickness is presented in four alternate ways.The first column shows boundary vein thickness relative to cladding veinthickness. The second column shows boundary vein thickness relative tothe selected pitch Λ of the cladding structure. The third column showsboundary vein thickness as a function of the selected operatingwavelength λ. These three measures are scalable and remain the same fora broad range of PBG fibre structure pitches and operating wavelengthsfor structures within the same bandgap. The fourth column shows absoluteboundary vein thickness in μm for an operating wavelength of 1.55 μm andmay be scaled according to Equations (1) and (2).

The fifth and sixth columns show values for percentage of light power inair η and F-factor respectively for the eleven structures. F-factor isshown in terms of Λ⁻¹ and is thus relevant to PBG fibres with periodiccladding structures. It is easy to calculate absolute F-factor in termsof μm⁻¹ for an absolute wavelength of 1.55 μm by dividing the F-valuesby 3 (since pitch is selected to be about 3 μm for a 1.55 μm operatingwavelength).

The light-in-air and F-factor of a particular structure is directlymeasurable. The method of measuring light-in-air involves taking anear-field image of light as it leaves the structure, overlaying it on ascanning electron micrograph (SEM) or atomic force microscopy (AFM)image of the structure and directly calculating the % light-in-air fromthe overlap of the two images, although care needs to be taken since thefield can vary rapidly across the boundary between air and glass. Suchtechniques will be readily apparent to those skilled in the art ofoptical fibre measurement techniques.

The light-in-air and F-factor can also be calculated more indirectly fora real fibre structure by the following method. A SEM or AFM image istaken of the cross-sectional structure of the fibre in question. Anaccurate representation of the structure, suitable for use in computermodelling, is obtained from the SEM by estimating the position of thestructural boundaries throughout the cross-section. Based on thisrepresentation, the mode field can be simulated by solving Maxwell'svector wave equation for the fibre structure, using known techniques. Inbrief, Maxwell's equations are recast in wave equation form and solvedin a plane wave basis set using a variational scheme. An outline of themethod may be found in Chapter 2 of the book “Photonic Crystals—Moldingthe Flow of Light”, J. D. Joannopoulos et al., ©1995 PrincetonUniversity Press. This knowledge of the electric and magnetic fielddistributions enables both the numerator and denominator in Equation (9)above to be calculated. The fraction η of light in air may also becalculated by superimposing the modelled mode on the modelled structure.

The very small size of the thin veins in the structure means that greatcare must be taken when interpreting an SEM image. The apparentthickness of a vein in the image may be slightly different from the truethickness, but the small discrepancy will have a large impact on thelight-in-air and F-factors determined from it. It is therefore advisableto confirm the validity of the process by which the model structure isdetermined from the SEM image, to yield a reliable fit. One way toconfirm the fit would be through spectral measurements of the loss ofthe fibre, which often show peaks at particular wavelengths due to modecrossings [see, for example, Smith et al., “Low-loss hollow-coresilica/air photonic bandgap fibre”, Nature, Vol. 424 pp 657-659, 7 Aug.2003].

The values for light power in air η and F-factor for a seven cell coredefect fibre are plotted in the graphs in FIGS. 9 a and 9 b respectivelyfor a fixed operating wavelength of 1550 nm. The horizontal axes ofthese plots are labelled as a core boundary thickness in terms of apercentage of the selected operating wavelength. In generating the plotsof FIGS. 9 a and 9 b, the fibre structure of FIG. 8 a was modelled on acomputer and the proportion of light in air η and the F-factor werecalculated for various boundary vein thicknesses t. Each point in theplots represents one thickness, according to the values in Table 1.

Similarly, the values of F-factor for nineteen-cell core defectstructures having varying core boundary thicknesses are plotted in thegraph in FIG. 9 c. This time, the horizontal axis of the plot islabelled as a core thickness in terms of a percentage of the claddingvein thickness. A graph of light in air for these structures is notshown, since it is evident that it would substantially mirror theF-factor graph. However, the highest identified light in air value,which is coincident with the lowest F-factor value, is in the region of99.7%. This value increases to about 99.95% for a similar 37-cell coredefect structure, which has a lowest F-factor of about 0.01 Λ⁻¹. Thebenefit of F-factor decreasing, and light in air fraction increasing,with increasing core defect diameter is at least to some degree temperedby a larger core potentially supporting more core-guided modes andsurface states, which can lead to an undesirable increase in modecoupling.

The plots demonstrate that η and F-factor vary considerably with coreboundary vein thickness even over the relatively small range ofthickness values modelled. In particular, the maximum value for η andthe minimum value of F-factor, for the seven cell core defectstructures, appear for boundary vein thicknesses in the range 0.3-0.37μm. This range is slightly below the calculated anti-resonant boundarythickness of 0.392 μm for the 6 μm tube.

Referring to the graph in FIG. 9 c, the optimum value of core boundarythickness for a nineteen cell core defect is in the range 0.354-0.425μm, which encompasses the modelled anti-resonant point for a 9 μm tube.

The foregoing technique of measuring F-factor and light in air fractionhas been shown to provide a reliable means for distinguishing betweengood and bad structures and ascertaining antiresonant core wallthicknesses. Obviously, a more rigorous numerical analysis might involveplotting η and F-factor for all values of wavelength within theband-gap, since the plots can vary slightly at different wavelengths,particularly in the vicinity of mode crossings, as describedhereinafter.

The simple circular core surround model for the properties of thefundamental guiding mode of band gap fibres is found to be more accuratefor nineteen-cell core defects than for seven-cell core defects at theselected operating wavelength of 1550 nm, and becomes increasinglyaccurate when the core boundary thickness approaches an optimumanti-resonance value. This is because the field intensity of thenormalized fundamental guided mode outside the core boundary and aircore region becomes smaller as the core size is increased andanti-resonance is approached. The field of the fundamental mode is thenless perturbed by the cladding: the effect of the cladding is simply torender the small field component which remains exterior to the coresurround evanescently decaying. As has already been mentioned, theslight non-circularity of the core surround in practical fibres is foundnot to change significantly the properties of the fundamental guidingmode from that of a perfectly circular geometry.

Following on from this, it will be apparent that different claddingstructures, in which different numbers or shapes of boundary vein (or,indeed, other forms of relatively high refractive index material) meetthe core boundary, will cause the effective boundary thickness to varyfor a given absolute boundary vein thickness. While it might berelatively complex to model exact anti-resonance for such boundaries,which may differ significantly from a tube or even a dodecagon, byfollowing the teachings provided herein, the skilled person will be ableto calculate η or F-factor and use either one as a proxy to design ananti-resonant boundary.

In considering in more detail the shape of the curve in FIGS. 9 a (lightin air percentage) and 9 b (F-factor), it is apparent that local minimaof the former and maxima of the latter occur at core vein thicknessesaround 16% and 25% of the operating wavelength λ. The present inventorsdo not believe, however, that these spikes coincide with resonances ofthe core boundary. By substituting an operating wavelength of 1550 nminto Equation (2), the first-order resonance peak should occur at anabsolute boundary thickness of around 0.74 μm, which equates to a valueof around 48.4% of the operating wavelength. Clearly, this value issignificantly higher than either value associated with the spikes inFIGS. 9 a and 9 b. The present inventors suggest that the spikes are dueto interactions between the mode being investigated and so-calledsurface modes near to the core boundary. This kind of interaction isalso identified in Müller, D. et al. “Measurement of photonic band-gapfiber transmission from 1.0 to 3.0 μm and impact of surface modecoupling.” QTuL2 Proc. CLEO 2003 (2003). This paper supports the presentinventors' view that mode power from the air-guided modes may couple tolossy surface modes, which concentrate in or near to the core boundary.The result is increased loss, attendant increased F-factor and reducedlight in air fraction. As already mentioned, the effect of modecrossings can also vary with wavelength. Indeed, it is found using thepreviously described circular core surround model that such modecrossings are suppressed for core thicknesses close to the anti-resonantvalue, but become abundant for core thicknesses away fromanti-resonance. This surface mode exclusion property associated with theanti-resonance renders the curves (for example as shown in FIG. 9) forF-factor and percentage of light in air smoother as they reach optimumvalues at core boundary thicknesses close to the anti-resonant point.

That an antiresonant core boundary is desirable for reducing the impactand/or number of surface modes in a PBG fibre is surprising andcounter-intuitive, particularly when one considers the prior art, forexample the teachings in the book “Photonic Crystals: Molding the Flowof Light”. From such a reference, the skilled man would understand thatsurface modes can form due to the inclusion of a defect in a PBFstructure; for example a hollow core defect in a PBG fibre. Afterappreciating this, it would appear sensible to include only a singledefect in the structure; where plural defects could lead to plural setsof surface modes. Hence, it would appear reasonable to form a coredefect boundary that, as closely as possible, matches the veins in thecladding structure. Otherwise, the core defect boundary might been‘seen’ by the light as an additional defect, or even a waveguide in itsown right, since it neither matches the core defect nor the cladding. Inother words, having a core defect boundary that is significantlydifferent, for example thicker in transverse cross section, than theindividual cladding veins of the PBG cladding structure, would not havebeen a natural choice for the skilled person who wanted to avoid theformation of surface modes.

In order to remove the peaks in FIGS. 9 a to 9 c, it is either necessaryto remove the surface states or adjust the operating point of therespective waveguide to avoid mode crossings. Moving the operating pointfor a given geometry can be achieved by varying the operating wavelengthwithin the band gap and/or adjusting the pitch Λ of the photonicband-gap structure. Clearly the avoidance of mode crossings facilitatedby a core surround close to anti-resonance will typically enable a widerwavelength bandwidth to be of practical use.

FIG. 10 a illustrates one way of arranging a stack of capillaries 1200to be drawn into a pre-form and fibre of the kind that is exemplified byFIG. 8. The cladding is formed by stacking round cross-sectioncapillaries 1205 in a close-packed, triangular lattice arrangement. Thecladding capillaries 1205 have an outer diameter of 1.04 mm and a wallthickness of 40 μm. The inner region 1210 of the stack contains a largediameter capillary 1215 having an outer diameter of 4.46 mm and a wallthickness of 105 μm. The large diameter capillary 1215 supports thecladding capillaries while the stack is being formed and eventuallybecomes part of the material that forms a core defect boundary 145. Theresulting structure, as shown in the SEM image of FIG. 11 a, has aboundary wall thickness in the region of 7% of the pitch, which isslightly below the optimum region for anti-resonance.

Interstitial voids 1220 that form between each triangular group of threecladding capillaries are each packed with a glass rod 1225, which has anouter diameter of 0.498 mm. The rods 1225 are inserted into the voids1220 after the capillaries have been stacked. The rods 1225 that arepacked in voids 1220 assist in forming cladding nodes 160, which have adiameter that is significantly greater than the thickness of the veinsthat meet at the nodes. Omission of a rod from a void in the claddingwould lead to the formation of a cladding node that has a significantlysmaller diameter.

The stack 1200 is arranged as described with reference to FIG. 10 a andis then over-clad with a further, relatively thick walled capillary (notshown), which is large enough to contain the stack and, at the sametime, small enough to hold the capillaries and rods in place. The entireover-clad stack is then heated and drawn into a pre-form, during whichtime all the interstitial voids at the boundary, and remaining voidsbetween the glass rods and the cladding capillaries, collapse due tosurface tension. The pre-form is, again, over-clad with a final, thicksilica cladding and is heated and drawn into optical fibre in a knownway. If surface tension alone is insufficient to collapse theinterstitial voids, a vacuum may be applied to the interstitial voids ofthe pre-form, for example according to the process described in WO00/49436 (The University of Bath).

The thickness of the boundary resulting from the stack in FIG. 10 a isreadily varied by using different thicknesses of large diametercapillary 1215.

FIG. 10 b is a diagram of a stack, similar to the stack shown in FIG. 10a, but this time suitable for making a nineteen-cell core defect fibre.As shown, an inner region of the stack is supported around a thickwalled, relatively large capillary, in place of nineteen claddingcapillaries; an inner capillary, the six capillaries that surround theinner capillary and the twelve capillaries that surround the sixcapillaries. The cladding capillaries have an outside diameter of about1.8 mm and a wall thickness of about 50 μm and the core tube has anoutside diameter of about 7.6 mm and a wall thickness of about 300 μm.

The stack shown in FIG. 10 b can be drawn down (which may involveapplying appropriate pressures to the various holes in the pre-form) toproduce a fibre as shown in the SEM image in FIG. 1 lb. The cladding ofthe fibre has a pitch Λ in the region of about 3.75-3.83 μm, a corediameter of about 17.7 μm and an average core thickness of about0.09-0.1 Λ, an AFF of about 0.92 (92%) and a value of d/Λ of about 0.97(where d in this case is the shortest distance between opposing sides ofa hexagonal cladding hole).

According to the plots in FIGS. 4 a, 4 b and 9 c, the anti-resonancepoint for a nineteen-cell core defect fibre is in the region of 0.4 μm(or 0.12 Λ). The core boundary thickness for the fibre structure shownin FIG. 11 b, therefore, is slightly below the anti-resonant point. Inorder to make a thicker core boundary, therefore, it would be necessaryto use similar fibre drawing conditions and a slightly thicker, largediameter, inner tube in the stack.

The graph in FIG. 12 is a plot of loss (in dB/km) against wavelength forthe fibre shown in the image of FIG. 1 lb. The plot was generated usingan optical spectrum analyser to measure transmitted power through alength of more than 1 km of fibre, and various cut-back lengths. As canbe seen, the loss is in the region of 2 dB/km over a significant band ofwavelengths about a centre frequency of about 1566 nm. Such a low losshas, hitherto, not been reported for hollow core photonic band-gapfibres. The lowest previously-reported loss is 13 dB/km. The presentfibre exhibits such a low loss while not even having an optimum coreboundary thickness. The present inventors are confident that a similarfibre having a slightly thicker core boundary, which is nearer to theanti-resonance point and has an attendant lower F-factor, will achievean even lower loss, for example even lower than 1 dB/km. In addition,with reference to the SEM image in FIG. 11 b, there is clearly scope toimprove the uniformity of the photonic band-gap structure in the fibre.Improved uniformity, both in the transverse and longitudinal planes, isreported in the prior art as a means to significantly reduce loss inband-gap fibres. The present inventors agree and believe that increaseduniformity will lead to significant reductions in loss, for example tobelow 0.5 dB/km or even below 0.2 dB/km, which is the approximate lossof standard, single mode optical fibre.

In addition, as described in the aforementioned paper “Low loss (1.7dB/km) hollow core photonic bandgap fiber”, the present inventorspredict that the loss of a fibre structure of the kind shown in FIG. 11b may be reduced to below 1 dB/km simply by scaling the dimensions ofthe structure for operation in the wavelength region of between 1800 nmand 2000 nm.

FIG. 13 is a diagram of an alternative embodiment of the presentinvention in which a dodecagonal core boundary varies in thickness aboutthe core, with the longer boundary veins being thicker than the shorterones. The effective thickness of the boundary is a function of the twothickness of boundary vein and their respective lengths as well as thesilica that joins to the outer surface of the boundary at boundarynodes.

FIG. 14 is a diagram of a further alternative embodiment of the presentinvention in which a dodecagonal core boundary has alternating short,thin core boundary veins and long, generally elliptical boundary veins,where the minor axis (or thickness) of the ellipses is significantlylonger than the thickness of the shorter sides. Hence, the effectivethickness of the boundary is a function of the two kinds of boundaryvein as well as the silica that joins to the outer surface of theboundary at boundary nodes.

The PBG fibre structures shown in FIGS. 13 and 14 may be manufacturedusing known stack and draw methods, wherein preforms are prepared withadditional silica rods in regions requiring greater volumes of silica inthe final fibre.

The skilled person will appreciate that the various structures describedabove may be manufactured using the described manufacturing process or aprior art processes. For example, rather than using a stacking anddrawing approach to manufacture, a pre-form may be made using a knownextrusion process and then that pre-form may be drawn into an opticalfibre in the normal way.

In addition, the skilled person will appreciate that while the examplesprovided above relate exclusively to PBG fibre cladding structurescomprising triangular arrays, the present invention is in no way limitedto such cladding structures. For example, the invention could relateequally to square lattice structures; or structures that are notclose-packed. In general, the inventors propose that given a claddingstructure that provides a PBG and a core defect in the claddingstructure that supports guided modes, the form of the boundary at theinterface between the core defect and the cladding structure will have asignificant impact on the characteristics of the waveguide, as describedherein.

The skilled person will appreciate that the structures described hereinfit on a continuum comprising a huge number of different structures, forexample having different combinations of core defect size, boundary veinthickness and, in general, boundary and cladding form. Clearly, it wouldbe impractical to illustrate each and every variant of PBG waveguidestructure herein. In particular, where numerical values or ranges ofvalues are given herein for a particular parameter, all combinationswith values or ranges of values of other parameters given herein aredisclosed unless such combinations are not physically possible. As such,the skilled person will accept that the present invention is limited inscope only by the present claims.

1-51. (canceled)
 52. An optical waveguide, comprising: a core,comprising an elongate region of relatively low refractive index; aphotonic bandgap structure arranged to provide a photonic bandgap over arange of wavelengths of light, the structure, in a transverse crosssection of the waveguide, surrounding the core and comprising elongaterelatively low refractive index regions interspersed with elongaterelatively high refractive index regions; and a relatively highrefractive index boundary at the interface between the core defect andthe photonic bandgap structure, the boundary having a thickness aroundthe core such that, in use, light guided by the waveguide is guided in atransverse mode in which, in the transverse cross-section, more than 95%of the guided light is in the regions of relatively low refractive indexin the waveguide.
 53. A waveguide as claimed in claim 52, in which theboundary has a thickness such that, in use, light guided by thewaveguide is guided in a transverse mode in which, in the transversecross-section, more than 1% of the guided light is in the regions ofrelatively low refractive index in the photonic bandgap structure.
 54. Awaveguide as claimed in claim 52, in which the boundary has a thicknesssuch that, in use, light guided by the waveguide is guided in atransverse mode in which, in the transverse cross-section, more than 50%of the guided light is in the region of relatively low refractive indexin the core.
 55. A waveguide as claimed in claim 52, in which theboundary has a thickness such that, in use, light guided by thewaveguide is guided in a transverse mode providing an F-factor of lessthan 0.23 μm⁻¹ for an operating wavelength of 1.55 μm, less than anequivalent F-factor value scaled for a different operating wavelength orless than 0.7 Λ⁻¹ for structures having a periodic cladding and a pitchΛ.
 56. An optical waveguide, comprising: a core, comprising an elongateregion of relatively low refractive index; a photonic bandgap structurearranged to provide a photonic bandgap over a range of wavelengths oflight, the structure, in a transverse cross section of the waveguide,surrounding the core and comprising elongate relatively low refractiveindex regions interspersed with elongate relatively high refractiveindex regions; and a relatively high refractive index boundary at theinterface between the core defect and the photonic bandgap structure,the boundary having a thickness around the core such that, in use, lightguided by the waveguide is guided in a transverse mode providing anF-factor of less than 0.23 μm⁻¹ for an operating wavelength of 1.55 μm,less than an equivalent F-factor value scaled for a different operatingwavelength or less than 0.7 Λ⁻¹ for structures having a periodiccladding and a pitch Λ.
 57. A waveguide according to claim 52, in whichthe boundary is anti-resonant at an operating wavelength of light.
 58. Awaveguide as claimed in claim 52, in which the boundary has asubstantially constant thickness around the core.
 59. A waveguide asclaimed in claim 52, in which the boundary has a thickness that variesaround the core, wherein the core boundary has a thickness t around atleast a proportion y of the boundary, where y>0.5.
 60. A waveguide asclaimed in claim 52, in which the boundary comprises, in the transversecross-section, a plurality of relatively high refractive index boundaryveins connected end-to-end around the boundary between neighbouringboundary nodes, each boundary vein being connected between a leadingboundary node and a following boundary node, with no nodes in between,and each boundary node being connected between two boundary veins and toa relatively high refractive index region of the photonic bandgapstructure.
 61. A waveguide according to claim 60, wherein each boundaryvein has a characteristic thickness substantially at the mid-pointbetween the two boundary nodes to which it is connected.
 62. A waveguideaccording to claim 60, wherein the characteristic thickness of at leastone boundary vein is at least 110% of the characteristic thickness of aplurality of the veins in the array of veins in the photonic band-gapstructure.
 63. A waveguide as claimed in claim 52, in which the arrayhas a characteristic primitive unit cell and a pitch Λ.
 64. A waveguideas claimed in claim 63, in which the boundary has a thickness t,wherein, t=uΛ for a proportion of the boundary y, where u>0.06 andy>0.5.
 65. A waveguide as claimed in claims 52, in which the coreboundary has a thickness t defined by${{\frac{a\quad\lambda}{4\sqrt{n_{HI}^{2} - n_{LO}^{2}}} \leq} = {{t \leq} = \frac{b\quad\lambda}{4\sqrt{n_{HI}^{2} - n_{LO}^{2}}}}},$where a=0.5 and b=1.75 and n_(HI) and n_(LOW) are the refractive indicesof the boundary and of the relatively low refractive index region of thecore, respectively.
 66. A photonic crystal fibre, comprising: anelongate, relatively low refractive index core; an elongate photonicbandgap structure surrounding the core and comprising, in the transversecross section, a lattice of relatively low refractive index regionsseparated by connected relatively high refractive index regions; and aconcentric boundary region, at the interface between the core and thephotonic bandgap structure, the core boundary region being generallythicker around its circumference than regions of relatively highrefractive index in the photonic bandgap structure.
 67. A waveguideaccording to claim 56, in which the boundary is anti-resonant at anoperating wavelength of light.
 68. A waveguide as claimed in claim 56,in which the boundary has a substantially constant thickness around thecore.
 69. A waveguide as claimed in claim 56, in which the boundary hasa thickness that varies around the core, wherein the core boundary has athickness t around at least a proportion y of the boundary, where y>0.5.70. A waveguide as claimed in claim 56, in which the array has acharacteristic primitive unit cell and a pitch Λ.
 71. A waveguide asclaimed in claim 56, in which the core boundary has a thickness tdefined by${\frac{a\quad\lambda}{4\sqrt{n_{HI}^{2} - n_{LO}^{2}}} \leq t \leq \frac{b\quad\lambda}{4\sqrt{n_{HI}^{2} - n_{LO}^{2}}}},$where a=0.5 and b=1.75 and n_(HI) and n_(LOW) are the refractive indicesof the boundary and of the relatively low refractive index region of thecore, respectively.